Apparatuses and processes for calculating options

ABSTRACT

The present invention introduces an apparatus and process which may be implemented on a vast variety of computer systems. The apparatus and process of the present invention use a computer system to receive and store data representative of a particular asset, a type of option (call or put), requested exercise price and a multitude of other variables related to the asset. The apparatus and process then generate data representative of an option premium. The data representative of the option may then be used for transacting an option, as the basis for determining a correlated expiring option premium, or to determine the premium of an asset relatable to a corresponding option. Other embodiments are also claimed and described.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.11/276,293, filed 22 Feb. 2006, which is a continuation of U.S. patentapplication Ser. No. 09/906,305 filed 16 Jul. 2001, now U.S. Pat. No.7,024,384 B2, which is a continuation of U.S. patent application Ser.No. 09/262,663 filed 4 Mar. 1999, now U.S. Pat. No. 6,263,321, which isa continuation-in-part of U.S. patent application Ser. No. 08/718,630filed Sep. 17, 1996, now U.S. Pat. No. 5,884,286, which is acontinuation-in-part of U.S. patent application Ser. No. 08/282,717filed 29 Jul. 1994, now U.S. Pat. No. 5,557,517. All of theabove-mentioned patent applications and patents are hereby incorporatedherein by reference as if fully set forth below.

FIELD OF INVENTION

The present invention relates generally to an apparatus and process forautomatically calculating options for use in a variety of markets, suchas commodities or securities markets.

BACKGROUND OF THE INVENTION

An “option” is generally used to hedge risk by providing the right topurchase or sell a commodity or other asset at a later time at a setprice with only limited obligations. An option is similar to aninsurance policy in that it insures that an asset may be purchased orsold at a later time at a set price in return for a premium, oftenreferred to as an option premium, which is generally a relatively smallpercentage of the current value of the asset. One type of option is a“call option.” A “call” option gives the purchaser of the option theright, but not the obligation, to buy a particular asset at a later timeat a guaranteed price, often referred to as the “exercise price.”Another type of option is a “put option”. A “put” option gives thepurchaser of the option the right, but not the obligation, to sell aparticular asset at a later time at the exercise price. (The “put”option may be thought of as giving the owner the right to “put” thesecurity into another's name at the exercise price.) In either instance,the seller of the call or put option is obligated to perform theassociated transactions if the purchaser chooses to exercise its option.

Options are utilized in a variety of asset-based transactions. Forexample, in the commodities market, commodity producers (e.g., farmers)often enter into option relationships with commodity users (e.g.,manufacturers) and speculators; in the real estate market, real estateowners often enter into option relationships with real estatepurchasers; and in the securities market, security holders often enterinto option relationships with security purchasers.

Commodity Market Examples

A commodity user such as a cereal manufacturer may need a certain amountof corn and wheat at a future date. The Cereal manufacturer, rather thanpurchasing the corn and wheat, may purchase a “call” option from aspeculator by rendering an option premium. The call option guarantees anexercise price for a set amount of corn and wheat at a future date. Thespeculator, in return for receiving the option premium, agrees to obtainthe set amount of corn and wheat and sell it to the cereal manufacturerat the exercise price at the future date.

If the price of the desired commodities increases, then the cerealmanufacturer will likely exercise the “call” option and obtain the setamount of commodities from the seller at the guaranteed exercise price.Therefore, by paying the option premium in advance of knowing the futurevalue of the commodities, the cereal manufacturer may save itself asubstantial amount of money. If the price of the desired commoditiesdoes not reach the exercise price then the cereal manufacturer will notexercise the call option and will purchase the commodities on the openmarket at the going price.

A commodity producer, such as a farmer, may plant his fields many monthsin advance of having a commodity ready for delivery. To guarantee a setfuture price for his commodity, the farmer may purchase a “put” optionfrom a speculator. Here, if the price of the farmer's commodities goesdown over the set period of time the farmer is guaranteed to receive aset amount of minimum income for his efforts from the speculator.

Prior art systems are only capable of transacting options which expireafter a certain period of “time”. The purchaser of a call or put optionusing the prior art systems only has the right to exercise the optionbefore it expires or on the expiration date.

As shown in FIGS. 8-11, for a set period of time, an option transactedusing a prior art system has some value associated with it depending onthe type of option, the current value of the asset relative to theexercise price and other variables. However, the moment after the optionexpires, a purchased option, as shown in FIGS. 8 and 9, is worthlesscausing an option purchaser who may have owned a valuable option one dayto own a worthless option the next day. Furthermore, not only is theoption worthless, but the purchaser of the call or put option is nolonger protected against future price fluctuations associated with theasset. On the other hand, as shown in FIGS. 10 and 11, a sold option,which might be falling in value, automatically rises to the value of theoption premium and removes all future risks to the option seller themoment after the option expires.

Turning to FIG. 8, a call option on shares of Company A is shown with anoption premium of $5 per share and an exercise price of $55 per share.Ignoring the effect of “time” and other nominal costs associated withtransacting options, the value of the options on the shares of Company Amay increase or decrease based on the current price of the shares. Forexample, if the current share price rose from $50 to $56, then the valueof the purchased call option would increase because it would be morelikely to be exercised at the $55 per share exercise price. Further, ifthe current share price rose to $60, then the value of the purchasedcall option would increase even more because the owner of the purchasedcall option could now purchase shares of Company A at the exercise priceof $55 and sell them for $60 on the open market resulting in a $5 pershare profit. Moreover, the value of the purchased call option wouldcontinue to increase if the current share-price of the shares of CompanyA continued to rise higher and higher. Accordingly, as long as thecurrent price of the asset (the shares of Company A) continues toincrease, the profits associated with the return on investment for apurchaser of a call option are unlimited. However, as might be expected,the exact opposite results for the seller of the call option (see FIG.10) in that the losses attributed to the seller of a call option areunlimited.

On the other hand, continuing to ignore the effect of “time,” if thecurrent share price dropped from $50 to $45, then the value of thepurchased call option would decrease because it would be less likely tobe exercised at the $55 per share exercise price. Moreover, as thecurrent share price dropped further, the purchased call option would beeven less likely to be exercised. However, unlike the situation abovewhere the value of the purchased call option continued to increase asthe current share price increased, for a purchased call optionassociated with an asset which decreases in value, the maximum lossassociated with the return on investment is limited to the optionpremium (for this example, $5 per share). Again, the exact oppositeresults for the seller of the call option in that the profits realizedby the seller of a call option are capped at the option premium.

Referring to FIGS. 9 and 11, similar yet opposite results may berealized by the purchaser and seller of a put option, respectively,using a prior art system for transacting options. Here, assume thatinvestor P purchases a put option from investors who sells the putoption on the shares of Company A with an exercise price of $45 in sixmonths in return for an option premium of $5 per share.

Here, again ignoring the effect of “time or other nominal costs,” if thevalue of the shares of Company A fell to $44, then the value of thepurchased put option (FIG. 9) would increase because it would be morelikely to be exercised. Moreover, if the value of the shares continuedto fall to $40, then the value of the purchased put option wouldincrease even more because the owner of the purchased put option wouldbe able to obtain shares of Company A at a price of $40 per share andsell these same shares at $45 per share by exercising its put optionresulting in a $5 per share profit. Accordingly, as long as the currentprice of the asset (the shares of Company A) continue to decrease, theprofits associated with the return on investment for a purchaser of aput option are limited to the exercise price (less the option premiumpaid) if the asset price fell to zero. However, the seller of the putoption (See FIG. 12) realizes potential losses equal to the exerciseprice (less the option premium received) if the asset price fell tozero.

On the other hand, if the current share price increases, then the valueof the purchased put option would decrease because it would be lesslikely to be exercised. However, regardless of how much the share priceincreased, the maximum loss associated with the return on investmentthat the purchaser of a put option would realize is limited to theoption premium. In contrast, the seller of the put option realizes amaximum profit of the option premium.

Based on the above examples, it should be readily apparent that,ignoring “time,” the purchaser of a call or a put option may essentiallyrealize an unlimited gain while limiting his or her potential loss tothe amount of the option premium. On the other hand, the seller of acall or a put option acts as an insurer by collecting the option premiumin return for insuring that the purchaser of the option will be able tobuy or sell the underlying asset at the exercise price. Thus, the Sellerassumes all of the risks. To reallocate the risks, the element of timeis used in option trading. The purchaser of an option is only allowed toexercise the option over a preset increment of “time”.

Referring again to FIGS. 8 and 9, even though a purchased call optionmay increase in value as the current price of the asset increases, thevalue of the call option whose current price has yet to reach theexercise price must always battle “time.” In other words, the closerthat the call option gets to its expiration date, the more “time” willhave a negative effect on the value of the purchased call option because“time” will be running out for the current price of the asset to reachthe exercise price. If the current price of the asset on the expirationdate is below the exercise price for the purchased call option theoption holder will (1) be left holding an option worth absolutelynothing and (2) be left unprotected in its efforts to buy a particularasset at a later “time.” Thus, the purchaser assumes much more of therisk when options are limited to set times.

Therefore, there exists a need in the art for a technique to limit therisk that an option purchaser must assume, which at the same time, isnot unfair to the option seller. More specifically, there exists a needin the art for an apparatus and process for calculating an option whichis not dependent on “time” and is a fair value for the option seller.The applicant refers to such an option as an “expirationless option.”

Current techniques for calculating options are based on finite timessuch as 3 months, 6 months, 9 months, and, at the most, 3 years. Inthese techniques, the maximum price of an expiring option is consideredto be the underlying security price. However, in actuality, the maximumprice for any expiring option is its expirationless counter-part whichis always less than the security price. For this reason, the probabilityspace of expiring options has been incorrectly determined in the currentart. This error helps explain inconsistencies in efficient markets suchas “volatility smiles,” where the theoretical price for anout-of-the-money option is higher than the actual price sellers arewilling to receive. This error in pricing is because the probabilitydistribution that is assumed in the current art is the value S, ratherthan the smaller value for an expirationless option. Therefore, thereexists a need in the art for an apparatus and process to calculateoption prices that are not based on the maximum price of the underlyingsecurity, but rather are based on the price of an expirationless optionthat is counterpart to the expiring option.

A margin position is a means for an investor to purchase the right toacquire a particular asset (e.g., security) for an indefinite(expirationless) amount of time without having to pay the entire valueof the asset at the time of purchase. An investor purchases the right toacquire the particular asset by opening a “long” margin position or a“short” margin position. A long margin position (also referred to as aconditional purchase) is opened when the investor expects the value ofthe asset to increase, and a short margin position (also referred to asa conditional sale) is opened when the investor expects the value of theasset to decrease.

As shown in FIG. 12, a long margin position investor realizes a ReturnOn Investment (“ROI”) equal to the current value of an asset when theinvestor closes the margin position less the value of the asset when heopened the margin positioned. Therefore, if the value of an assetincreases from $20 to $30, then the long margin position investorrealizes a $10 profit when it closes the margin position. However, ifthe value of the asset decreases to $5, then the same investor realizesa $15 loss.

On the other hand, as shown in FIG. 13, a short margin position investorrealizes a ROI equal to the value of the asset when the investor openedthe margin position less the value of the asset when it closes themargin position. Therefore, if the value of an asset decreases from $20to $5, then the short margin position investor realizes a $15 profitwhen it closes the margin position. However, if the value of the assetincreases to $30, then the same investor realizes a $10 loss. Thesemargin positions, both long and short, may or may not have an interestcost calculated on the value of the conditional sale or purchase.

A margin price in the securities market for an expirationless option ona particular asset is usually much higher than an option premium for anexpiring option on the same asset. One reason for the substantialdifference between the margin requirement and the option premium for anexpiring option is that the entity (e.g., exchange or broker) offeringthe margin position essentially assumes more risk because, unlike theexpiring option, the margin position does not automatically expire aftera preset period of “time,” (unless, of course, the underlying assetexpires, such as a futures or commodity contract). Additionally, whilean option purchaser has the right but not the obligation to execute thecontract, each party in a margin position is obligated to perform.

Since any expiring asset must be a derivative of or represent acontingent claim on a nonexpiring asset, the margin position is assumedto be on the base of a non-expiring asset. In the case of a futurescontract on corn, though the margin position is actually for the futurescontract which will expire, this margin requirement can be demonstratedto actually represent the margin requirement for the corn, or baseasset, as well. Using current techniques, a change in the futurescontract is accomplished by “rolling over”, or exchanging one contractfor another to maintain the maximum future date of delivery or sale. Thepresent invention will make this unnecessary.

Unlike an option premium, the margin requirement is essentiallyrefundable to the investor of a margin position. This refund is realizedin that the margin requirement is applied to the purchase price (currentvalue) at the time the investor of a margin position closes the marginposition. Entities responsible for regulating margin positions(unscientifically) select a margin requirement balancing the demand ofinvestors, speculators and hedgers with the protection of the respectivemarket from default risk. These entities typically present marginrequirements either as a fixed dollar amount (margin amount) associatedwith a particular asset or a fixed percentage (margin percentage) of thecurrent price (value) of the particular asset.

A swap is a type of security transaction that is typically based onlarge amounts of money or securities wherein the parties to the swapexchange risks based on a notional amount. For instance, a swap mayinclude Party A agreeing to pay a fixed interest rate on a certainamount of money (i.e., 100,000,000) to Party B, in exchange for Party Bagreeing to pay a floating interest rate based on the same amount ofmoney to Party A. Generally, the floating interest rate is based on anindex, such as the T-bill rate, plus a fixed offset. As the underlyingindex fluctuates, the amount of money exchanged between Party A andParty B also fluctuates. However, the underlying amount of money, the$100,000,000, does not exchange hands.

Expirationless put and call option prices, because they have to be equalat the money, or where the current security price equals the exerciseprice, are arbitrized results. This is because the value of Americanoptions must equal the value of a replicating portfolio to avoidarbitrage opportunities and be consistent with economic equilibrium.Expirationless options are equivalent to a “swap” on the upsidepotential on the underlying security for the down side potential on theunderlying security, or vice versa. Expirationless options can beconsidered a financial swap where the notional value is the underlyingsecurity price. Thus, there exists a need in the art for an apparatusand a process for calculating the price of an expirationless option thatcan be used as the basis of a swap agreement.

Experts in the securities market and other markets dealing with optionshave concluded for many years that any system for transacting an optioncan only generate an option premium, which is fair to both the purchaserand seller of the option, if data representing the “time” in which theoption expires is input into the system. More specifically, allalgorithms that have been derived for generating fair option premiumsinclude a variable for “time”. Such algorithms include the Black-Scholesand Binomial Pricing. While some professionals in the securities marketshave discussed the pricing of expirationless options, they have ignoredthe arbitrized requirements that the put and call be equal at the moneyand have only focused on when and under what conditions exercise wouldbe optimal. They have further ignored the equality of volatility andinterest rate costs between expirationless options and the underlyingsecurity. This is a critical omission since, under the assumptions inthe current art concerning rational expectations and the absence ofeconomic dominance, the interest rate and volatility assumptions in anoption position equivalent to the underlying security demands equalityof volatility and interest rates between the expirationless option andthe underlying security.

Moreover, not only is there a need for a system capable of transacting afairly calculated premium for an option not dependent on “time,” butthere is a further need for such a system to automatically transactpurchases and sales of expirationless options instantaneously whilehandling (1) the constantly changing current asset prices and othervariables associated with the option premium pricing and (2) the highvolume (millions) of daily options transacted in the securities marketand other markets.

The above-referenced shortcomings, and other shortcoming of the priorart systems for calculating and transacting options that expire areeffectively overcome by the present invention, as described in furtherdetail below.

SUMMARY OF INVENTION

The present invention includes an apparatus and a process forcalculating and transacting options. In addition, the present apparatusand process for calculating option prices may be used in calculating andtransacting any asset which can be constructed as an individual orseries of options, regardless of their expiration date.

The present invention may be applied for calculating expirationlessoptions and option prices in the securities market, as well as a varietyof other asset-based markets. It should be understood that references tothe “present invention” are references to various embodiments of thepresent invention.

The present invention takes advantage of the inefficiency associatedwith the unscientifically selected margin requirements. Morespecifically, the present invention is able to combine theexpirationless feature of the margin position and the limited risk ofthe expiring option by recognizing that, because the margin requirementis unscientifically selected, a price (an option premium) exists thatwould cause many dealing in margin positions and expiring options tofind great benefits in transacting expiration less options.

The present invention takes advantage of the unscientifically selectedmargin requirements by recognizing a particular relationship betweenmargin positions and options. As shown in FIG. 14, a long marginposition is equivalent to a purchased expiring call option and a soldexpiring put option when the effect of “time” is discounted.Additionally, as shown in FIG. 15, a short margin position is equivalentto a sold expiring call option and a purchased expiring put option. Insum, if the effect of “time” is discounted, an entity allowing aninvestor to open a margin position (e.g., a long margin position), is inthe same position that it would be if it simply allowed an investor topurchase an expiring option (e.g., a call) and sell an expiring option(e.g., a put).

A significant feature of the present invention is that it is able todiscount the effect of “time” to allow a margin position to beequivalent to a purchased and sold option, as described above.Specifically, the present invention is able to utilize anyone of themultitude of expiring option algorithms for determining fair expiringoption premiums, as mentioned in the Background of the Invention, todiscount the effect of “time.”

All expiring option premium algorithms, in addition to including a“time” variable, include readily observable variables, such as thecurrent value (price) of the asset, the historic price volatility of theasset (the standard deviation of the asset's historic price movement)and the current risk-free interest rate (the rate of return withoutdefault risk, such as a U.S. government T-Bill rate). Further, allexpiring option premium algorithms include variables for the exerciseprice.

Accordingly, the present invention uses the expiring option premiumalgorithms to discount the effect of “time” according to the followingprocess: (1) the exercise price is set equal to the current price of theasset and (2) the option premium is set equal to the margin requirementfor the asset. The present invention then uses the expiring optionpremium algorithm to generate the anticipated point in “time” (impliedtime) in which an expiring option would expire if the purchaser paid anoption premium equal to the unscientifically set margin requirement ofthe asset and if the exercise price was equal to the current asset price(as it is for a margin position at the moment it is opened).

The present invention utilizes the above process because the exerciseprice is always equal to the current asset price at the moment when themargin position is opened, and this is the point in time when aninvestor of a margin position would gladly pay an inflated optionpremium equal to the margin position requirement to limit his risk.Accordingly, the present invention is able to discount “time” to price apurchased and sold option such that they are equivalent to a marginposition at the point where the asset price is assumed equal to theexercise price.

After the implied time value is generated, the present invention setsthe time value in the expiring option premium algorithm equal to theimplied time value. The present invention then generates anexpirationless option premium based on the particular exercise priceselected by the investor.

The present invention may be implemented on a vast variety of computersystems. More particularly, the present invention employs a computersystem to receive and store data representative of the particular asset,a type of option (call or put), a requested exercise price and themultitude of other variables related to transacting an expirationlessoption on the asset. Then, responsive to the data received, the presentinvention uses the computer system to generate data representative of anexpirationless option premium, and to transact the expirationless optionusing the expirationless option premium.

In use, when a user wishes to purchase or sell an expirationless option,the user is prompted to input data representative of the asset, the typeof option and the requested exercise price for the asset, into akeyboard or other means of the computer system. The apparatus andprocess of the present invention then prompt the user to enter certainother data related to transacting an expirationless option on the asset.The certain other data includes the current price for the asset on theopen market, the historic price volatility of the asset, the currentrisk-free interest rate and the margin requirement associated with theasset. Because this data typically changes frequently, the presentinvention may alternatively receive this data from one or more datasource (e.g., a database or real-time quote service such as S&PCornStock), connected to the computer system of the present invention.After all of the data is received, it is stored on a storage medium ofthe computer system.

The present invention then uses one of the expiring option premiumalgorithms to generate the data representative of the expirationlessoption premium. More specifically, the present invention temporarilysets the option premium variable of these algorithms to the marginrequirement data, temporarily sets the exercise price variable of thesealgorithms to the current asset price data and generates data for theimplied time of these algorithms. The present invention then uses theimplied time data and the exercise price data input by the user togenerate the data for the option premium variable of these algorithms.

The option premium data generated is the expirationless option premiumused to transact the expirationless option for the particular asset.Accordingly, the option premium data is output for use in completing theexpirationless option transaction.

The present invention is particularly important to those who wish toprotect themselves against price swings for indefinite periods of“time.” In other words, individuals and entities may now concernthemselves solely with the future price of an asset, and ceaseconcerning themselves with the seemingly impossible task of predictingthe “time” in which the asset may hit that price.

For example, a cereal manufacturer whose cereal prices to its customersdepend significantly on the price in which they are able to purchasewheat, can now better assure their customers of steady cereal prices bypurchasing an expirationless call option using the present invention.More specifically, the cereal manufacturer can now ensure itself that itmay continue to purchase wheat at or below a certain price (the exerciseprice), regardless of the “time” in the future when the price of wheatrises above the exercise price. Referring to FIG. 16, by utilizing thepresent invention, in return for the option premium, the cerealmanufacturer is able to purchase an expirationless call option which hasunlimited upside potential, limited downside potential (the optionpremium) and never becomes worthless.

On the other hand, a farmer whose family depends on being able to sellhis entire crop of wheat for a set minimum price would benefitsignificantly. Specifically, the farmer who was unable to predictwhether wheat prices might drop next year or in five years may purchasean expirationless put option using the present invention to ensure thathis wheat will be purchased at a certain price (the exercise price)regardless of the “time” in the future when the price of wheat dropsbelow the exercise price. Referring to FIG. 17, by utilizing the presentinvention, in return for an option premium, the farmer is able topurchase an expirationless put option which has unlimited upsidepotential, limited downside potential (the option premium) and neverbecomes worthless.

Another aspect of the present invention is that it is capable ofhandling constantly changing current asset prices and other variablesassociated with generating the option premium price and transacting theexpirationless option. As described above, by using one or more datasource, data from a variety of places, regardless of location, may beconstantly updated and stored for use in generating the option premiumprice at any given moment in time.

A further aspect of the present invention is that it is capable ofautomatically and essentially instantaneously transacting anexpirationless option in the securities market and other marketsthroughout the world. This is especially important in the securitiesmarket because millions of option contracts are typically transacteddaily. This feature is also important because of the volatility of thevariables used to generate the option premium price. This makes theessentially instantaneous transaction capability imperative, especiallyin the securities market.

A yet further aspect of the present invention is that it is capable ofhandling extinction bands. An extinction band is a price higher than theexercise price for a put option and lower than the exercise price for acall option. The extinction band price is selected because a particularentity responsible for exchange management may wish to implementexpirationless options without significantly increasing record-keepingrequirements for the respective exchange. By introducing extinctionbands, or forced closure of an expirationless option based not on time,but on the distance of the exercise price from the current asset price,an exchange may retain the aforementioned benefits of expirationlessoptions for their members without significantly increasing recordkeeping requirements. The pricing algorithm for this variant of theexpirationless option assumes that both the band, the maximum distanceof the exercise price from the asset price and the extinction date (orthe effective date of measurement of the exercise price from the currentasset price) for these options is known. If these variables are notknown, then the expirationless option with extinction bands is pricedexactly as the expirationless option without extinction bands.

A yet further aspect of the present invention is that it is capable offacilitating the determination of conventional expiring option premiumsutilizing the expirationless option price as the maximum price for theexpiring option. This allows for more accurate determination of theoption price than is possible using the underlying security price as themaximum price of an expiring option.

Yet another aspect of the present invention is that it is capable offacilitating the accurate determination of premiums for any financialinstrument which can be expressed in terms of an option or combinationof options. In order to determine a premium for a financial instrument,the premiums for corresponding option or options are first determinedutilizing the corresponding expirationless option price. The expiringoption premiums are then relatable to the premiums of the relatedfinancial instrument as appropriate for the instrument type.

Examples of financial instruments which may be determined utilizing thepresent invention include, but are not limited to equity, bonds,futures, forwards and swaps.

The aforementioned and other aspects of the present invention aredescribed in the detailed description and attached illustrations whichfollow.

BRIEF DESCRIPTION OF THE DRAWINGS

For a fuller understanding of the invention, reference should be made tothe following detailed description, taken in connection with theaccompanying drawings, in which:

FIG. 1 depicts a diagram of an exemplary computer system forimplementing the present invention.

FIG. 2 depicts components of an end user workstation for the computersystem of FIG. 1 for implementing the present invention.

FIG. 3 depicts components of a server for the computer system of FIG. 1for implementing the present invention.

FIG. 4 depicts a flow diagram of an exemplary embodiment for the MainModule of the present invention.

FIG. 5 depicts a flow diagram of an exemplary embodiment for the CALCmodule of the present invention, which calculates the expirationlessoption premium ignoring extinction bands.

FIG. 6 depicts a flow diagram of an exemplary embodiment for theDATA_ENTRY module of the present invention, which prompts the user toenter certain data for transacting the expirationless option.

FIG. 7 depicts a flow diagram of an exemplary embodiment for the CALC_Emodule of the present invention, which calculates the expirationlessoption premium with extinction bands.

FIG. 8 depicts a graph which illustrates the potential Return onInvestment (ROI) versus the Value of an Asset (Asset Value) for apurchased expiring option transacted on a prior art system.

FIG. 9 depicts a graph which illustrates the potential ROI versus theAsset Value for a purchased expiring put option transacted on a priorart system.

FIG. 10 depicts a graph which illustrates the potential ROI versus theAsset Value for a sold expiring option transacted on a prior art system.

FIG. 11 depicts a graph which illustrates the potential ROI versus theAsset Value for a sold expiring put option transacted on a prior artsystem.

FIG. 12 depicts a graph which illustrates the potential ROI versus theAsset Value of a long margin position.

FIG. 13 depicts a graph which illustrates the potential ROI versus theAsset Value of a short margin position.

FIG. 14 illustrates the equivalent relationship between a long margin isposition and a purchased call expirationless option (expiring optionwith time discounted) plus a sold put expirationless option (expiringoption with time discounted).

FIG. 15 illustrates the equivalent relationship between a short marginposition and a sold call expirationless option (expiring option withtime discounted) plus a purchased put expirationless option (expiringoption with time discounted).

FIG. 16 depicts a graph which illustrates the potential ROI versus theAsset Value of a purchased call expirationless option transacted usingthe apparatus and process of the present invention.

FIG. 17 depicts a graph which illustrates the potential ROI versus theAsset Value of a purchased put expirationless option transacted usingthe apparatus and process of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

The various aspects of the present invention may be implemented onnumerous types of computer systems, but is preferably implemented on aclient/server network 100 as shown in FIG. 1. The client/server network100 includes a server 110 connected to a plurality of clients 120, alsoknown as end-user workstations, and a data source 130 running on a tokenring environment.

As shown in FIG. 2, each end user workstation 120 may include amicroprocessor 210, a display 220, a keyboard 230, a mouse 240, aprinter 260, and a storage medium 250 (e.g., a disk array, tape, opticaldrive, tape drive or floppy drive).

As shown in FIG. 3, each server 110 may include a microprocessor 310 anda storage medium 350. The server may use Microsoft NT or peer-to-peerwith one peer dedicated as a server or their equivalent.

Data sources 130 may be a Quotron system or its equivalent, which mayregularly receive data via satellite communications 135, land lineconnections (e.g., a modem) 137 or the like. However, any other sourcecapable of receiving and providing data relevant to transacting theexpirationless option may be used in the present invention.

An exemplary client/server network suitable for implementing aspects ofthe present invention is a Windows NT PC LAN. These clients, servers,and client/server networks are mentioned for illustrative purposes onlyand, as may be appreciated by one of ordinary skill in the art, suitableequivalents may be substituted.

In an exemplary embodiment, when a user wishes to purchase or sell anexpirationless option related to a particular asset, the user may viewthe display 220 of the end user workstation 120 to obtain instructionson how to transact the expiration less option contract.

Referring to FIG. 4, at step 410 of the Main Module, the display 220displays a prompt requesting the user to indicate when the user is readyto transact the expirationless option. By pressing the ENTER key on thekeyboard 230 or clicking on a START box on the display 220 with themouse 240, the present invention starts its operation of transacting theexpirationless option by proceeding to step 420. For simplicitypurposes, it may be assumed that the microprocessor 210 of the end-userworkstation 120 and the microprocessor 310 of the server 110 coordinateall tasks of the end-user workstation 120 and server 110 of the computersystem, respectively, and all tasks between the two.

At step 415, the user is prompted to input data representative of aparticular asset. Upon receiving the data representative of a particularasset, the present invention proceeds to step 420.

At step 420, the user is prompted to select which option pricingalgorithm he or she wishes to use to transact the expirationless option.Such algorithms include, but are not limited to, the Black-Scholes, theBinomial Pricing, the Finite Difference and the Analytic Approximationalgorithms. These algorithms are widely used in connection withdetermining expiring option premiums and are available in bothproprietary and shareware software from Montgomery InvestmentTechnology. The option prices provided in this detailed description weredetermined using this free Internet service, and demonstrate that anyoption pricing algorithm may be used to determine expirationless optionprices.

For example, the Black-Scholes algorithm is:

$c = \frac{\left\lbrack {\sum\limits_{j = 0}^{n}\; {\left( \frac{n!}{{j!}{\left( {n - j} \right)!}} \right){p^{j}\left( {1 - p} \right)}^{n - j}{\max \left\lbrack {0,{{u^{j}d^{n - j}S} - K}} \right\rbrack}}} \right\rbrack}{r^{n}}$

Where:

-   -   c=OPT_PREM=the option premium    -   S=ASSET_PRICE=the current price for a particular asset    -   X=X_PRICE=the exercise price    -   r=T_BILL=the current risk-free interest rate    -   s=VOLATLTY=the standard deviation of the historic asset price    -   movement commonly referred to as the asset's volatility.

In another example, the Binomial Pricing algorithm is:

$c = {{S \cdot {\int_{- \infty}^{\frac{{\ln {(\frac{S}{X})}} + {{\lbrack{r + {(\frac{\sigma^{2}}{2})}}\rbrack}T}}{\sigma \sqrt{T}}}{\frac{1}{\sqrt{2\; \pi}}^{\frac{- z^{2}}{2}}\ {z}}}} - {^{- {rT}}{X \cdot {\int_{- \infty}^{\frac{{\ln {(\frac{S}{X})}} + {{\lbrack{r - {(\frac{\sigma^{2}}{2})}}\rbrack}T}}{\sigma \sqrt{T}}}{\frac{1}{\sqrt{2\; \pi}}^{\frac{- y^{2}}{2}}{y}}}}}}$

Where:

-   -   c=OPT_PREM=the option premium    -   S=ASSET_PRICE=the current price for a particular asset    -   K=X_PRICE=the exercise price    -   r=T_BILL=the current risk-free rate    -   n=the number of periods (the time) until expiration (for an        expiring option)

p=(r−d)/(u−d)

-   -   u=minimum value of an upward movement in the price of the        underlying asset (e.g., $⅛^(th) in most stocks), and    -   d=minimum value of a downward movement in the price of the        underlying asset ($0.0001 in most futures or commodities)    -   Note: u and d are generally established by the exchange and may        be    -   stored in a storage medium for access or simply input into the        system on an as needed basis.

Further, as one of ordinary skill in the art would readily appreciate,other related expiring options algorithms may be used to transact anexpirationless option. Upon receiving a number related to the user'sselected algorithm processing continues at step 430. In an alternativeembodiment step 420 may be removed entirely by only using a singleoption algorithm.

At step 430, the user is prompted to input whether or not it wishes toinclude extinction bands in the expirationless option transaction. Ifthe user selects no, then processing continues at step 500, otherwiseprocessing continues at step 700.

Referring to FIG. 5, at step 500 the CALC Module is executed. The CALCModule is used to calculate the expirationless option premium ignoringextinction bands. Of course, if used exclusively in markets or onexchanges without extinction bands, step 430 may be removed entirely.

Processing then continues at step 600 where the DATA_ENTRY Module isexecuted. The DATA_ENTRY Module, as shown in FIG. 6, is used to promptthe user to input data and to accept the data input by the user.

At step 601, the user is prompted to input the current price for theparticular asset. The user may obtain the current price for theparticular asset from a variety of sources, such as the data source 130.At step 602, it is determined whether the current price of the asset hasbeen received. If not, then processing returns to step 601, otherwisethe current price of the asset received is stored in the ASSET_PRICEvariable in the storage medium 250 and processing continues at step 603.

In another embodiment, steps 601 and 602 may be replaced by a step whichautomatically accesses the current price for the particular asset fromthe data source 130. In yet another embodiment, steps 601 and 602 may bereplaced by a step which automatically accesses the current price forthe particular asset from the storage medium 350 of the server 110 whichmay be updated automatically by the data source 130 or manually by anadministrator of the network.

At step 603, the user is prompted to input the current risk-freeinterest rate. The user may obtain the current risk-free interest ratefrom a variety of sources, such as the data source 130. At step 604, adetermination is made as to whether the current risk-free interest ratehas been received. If not, then the processing continues at step 603,otherwise the current risk-free interest rate received is stored in theT BILL variable in the storage medium 250 and processing continues atstep 605.

In another embodiment, steps 603 and 604 may be replaced by a step whichautomatically accesses the current risk-free interest rate from the datasource 130. In yet another embodiment, steps 603 and 604 may be replacedby a step which automatically accesses the current risk-free interestrate from the storage medium 350 of the server 110 which may be updatedautomatically by the data source 130 or manually by an administrator ofthe network.

At step 605, the user is prompted to input the standard deviation of theprice movement related to the asset known as the “historic pricevolatility of the asset.” The user may obtain the historic pricevolatility of the asset from a variety of sources, such as the datasource 130. At step 606, a determination is made as to whether thehistoric price volatility of the asset has been received. If not, thenthe processing continues at step 605, otherwise the historic pricevolatility of the asset received is stored in the VOLATLTY variable inthe storage medium 250 and processing continues at step 607.

In another embodiment, steps 605 and 606 may be replaced by a step whichautomatically accesses the historic price volatility of the asset fromthe data source] 30. In yet another embodiment, steps 605 and 606 may bereplaced by a step which automatically accesses the historic pricevolatility of the asset from the storage medium 350 of the server 110which may be updated automatically by the data source 130 or manually byan administrator of the network.

At step 607, the user is prompted to input the exercise price for theparticular asset. At step 608, a determination is made as to whether theexercise price of the asset has been received. If not, then processingcontinues at step 607, otherwise the exercise price of the assetreceived is stored in the X_PRICE variable in the storage medium 250 andprocessing continues at step 609.

At step 609, the user is prompted to input the option type (either acall option or a put option). At step 610, the present invention thenverifies whether the option type has been received. If not, then theprocessing returns to step 609, otherwise the processing stores theoption type under the OPT_TYPE variable in the storage medium 250 andproceeds to step 611.

At step 611, the user is prompted to input the margin requirement(margin amount or margin percentage) related to the particular asset.The user may obtain the margin requirement from a variety of sources,such as the data source 130. At step 612, a determination is made as towhether the margin requirement for the asset has been received. If not,then processing returns to step 611, otherwise the margin requirementfor the asset received is stored in the MARGIN variable in the storagemedium 250 and processing continues at step 699, and then to step 510 ofthe CALC Module at FIG. 5.

In another embodiment, steps 611 and 612 may be replaced by a step whichautomatically accesses the margin requirement from the data source 130.In yet another embodiment, steps 611 and 612 may be replaced by a stepwhich automatically accesses the margin requirement from the storagemedium 350 of the server 110 which may be updated automatically by thedata source 130 or manually by an administrator of the network.

At step 510, the temporary option premium is equated to the value of themargin requirement (MARGIN) and stored in the TEMP_OPT_PREM variable inthe storage medium 250. Processing then continues at step 520, where atemporary exercise price is set equal to the current price of the asset(ASSET_PRICE) and the temporary exercise price is stored under theTX_PRICE variable in the storage medium 250. Processing then continuesat step 530.

At step 530, the implied time for the expirationless option isdetermined using the option pricing algorithm selected at step 420. Theimplied time is then stored in the IMPLD_T variable in the storagemedium 250. Processing then continues at step 540.

At step 540, the actual option premium for the expirationless option isdetermined by again using the option pricing algorithm selected at step420, the X_PRICE selected at step 607, and the implied time value(IMPLD_T). Processing then continues at step 440 of the Main Module atFIG. 4.

Referring back to step 430, if the user selects to include extinctionbands in the expirationless option transaction, processing continues atstep 700 of the CALC_E module. Referring to FIG. 7 at step 700 theCALC_E module calculates the expirationless option premium taking intoaccount extinction bands.

Processing then continues at step 600 at the DATA_ENTRY Module. Again,the DATA_ENTRY Module, as shown in FIG. 6, is used to prompt the user toinput data and to accept the data input by the user.

At step 601, the user is prompted to input the current price for theparticular asset. The user may obtain the current price for theparticular asset from a variety of sources, such as the data source 130.At step 602, a determination is made as to whether the current price ofthe asset as been received. If not, then processing returns to step 601,otherwise the current price of the asset received is stored in theASSET_PRICE variable in the storage medium 250 and processing continuesat step 603.

In another embodiment, steps 601 and 602 may be replaced by a step whichautomatically accesses the current price from the data source 130. Inyet another embodiment, steps 601 and 602 may be replaced by a stepwhich automatically accesses the current price from the storage medium350 of the server 110 which may be updated automatically by the datasource 130 or manually by an administrator of the network.

At step 603, the user is prompted to input the current risk-freeinterest rate. The user may obtain the current risk-free interest ratefrom a variety of sources, such as the data source 130. At step 604, adetermination is made as to whether the current risk-free interest ratehas been received. If not, then processing returns to step 603,otherwise the current risk-free interest rate received is stored in theT_BILL variable in the storage medium 250 and processing continues atstep 605.

In another embodiment, steps 603 and 604 may be replaced by a step whichautomatically accesses the current risk-free interest rate from the datasource 130. In yet another embodiment, steps 603 and 604 may be replacedby a step which automatically accesses the current risk-free interestrate from the storage medium 350 of the server 110 which may be updatedautomatically by the data source 130 or manually by an administrator ofthe network.

At step 605, the user is prompted to input the standard deviation of theprice movement related to the asset known as the “historic pricevolatility of the asset.” The user may obtain the historic pricevolatility of the asset from a variety of sources, such as the datasource 130. At step 606, a determination is made as to whether thehistoric price volatility of the asset has been received. If not,processing returns to step 605, otherwise the historic price volatilityof the asset received is stored in the VOLATLTY variable in the storagemedium 250 and processing continues at step 607.

In another embodiment, steps 605 and 606 may be replaced by a step whichautomatically accesses the historic price volatility of the asset fromthe data source 130. In yet another embodiment, steps 605 and 606 may bereplaced by a step which automatically accesses the historic pricevolatility of the asset from the storage medium 350 of the server 110which may be updated automatically by the data source 130 or manually byan administrator of the network.

At step 607, the user is prompted to input the exercise price for theparticular asset. At step 608, the processing then verifies whether theexercise price of the asset has been received. If not, then theprocessing returns to step 607, otherwise the processing stores theexercise price of the asset received under the X_PRICE variable in thestorage medium 250 and proceeds to step 609.

At step 609, the user is prompted to input the option type (either acall option or a put option). At step 610, a determination is made as towhether the option type has been received. If not, then processingreturns to step 609, otherwise the option type is stored in the OPT_TYPEvariable in the storage medium 250 and processing continues at step 611.

At step 611, the user is prompted to input the margin requirement(margin amount or margin percentage) related to the particular asset.The user may obtain the margin requirement from a variety of sources,such as the data source 130. At step 612, a determination is made as towhether the margin requirement for the asset has been received. If not,then processing returns to step 611, otherwise the margin requirementfor the asset received is stored in the MARGIN variable in the storagemedium 250 and processing continues at step 699, and then to step 510 ofthe CALC_E Module at FIG. 7.

In another embodiment, steps 611 and 612 may be replaced by a step whichautomatically accesses the margin requirement from the data source 130.In yet another embodiment, steps 611 and 612 may be replaced by a stepwhich automatically accesses the margin requirement from the storagemedium 350 of the server 110 which may be updated automatically by thedata source 130 or manually by an administrator of the network.

At step 710, the user is prompted to input whether or not it wishes todetermine the extinction band in percentages or in dollars. If the userselects percentages, then processing continues at step 720, otherwiseprocessing continues at step 750.

At step 720, the user is prompted to input the percentage price movementto be used to determine the extinction band and the percentage is storedin the PERCENT variable in the storage medium 250. Processing thencontinues at step 725, where it determines whether the expirationlessoption type (OPTION_TYPE) is a “call” or a “put”. If the expirationlessoption is a “call,” then processing continues at step 730, otherwiseprocessing continues at step 735.

At step 730, the current asset price (ASSET_PRICE) for the “call” optionis set to the current asset price (ASSET_PRICE) multiplied by the valuecomposed of the percentage price movement (PERCENT) plus one. On theother hand, at step 735, the current asset price (ASSET_PRICE) for the“put” option is set to the current asset price (ASSET_PRICE) multipliedby the value composed of the percentage price movement (PERCENT) minusone.

Processing then proceeds from step 730 or step 735 to step 775.Processing, at step 775, accesses and receives the extinction date forthe particular asset (EXT_DATE) which has been set by the exchange andstored by the system administrator from the storage medium 250 or 350.Of course, the extinction date could also be manually input by the userof the present invention, who could manually input the extinction dateset by the exchange each time the system is used. Processing thencontinues step 780.

At step 780, processing then determines the option premium for theexpirationless option taking into account the extinction band by againusing the option pricing algorithm selected at step 420 and setting thevalue of time until expiration in the algorithm to EXT DATE. Processingthen continues at step 799.

Referring back to step 710, if the user selects to use dollars todetermine the extinction band, then the invention proceeds to step 750.At step 750, the user is prompted to input the minimum dollar amountprice movement to be used to determine the extinction band, and thedollar amount price movement is stored in the TICK variable in thestorage medium 250. At step 755, processing then sets the BAND variableto dollars.

Processing then continues at step 760, where a determination is made asto whether the expirationless option type (OPTION_TYPE) is a “call” or a“put” option. If the expirationless option is a “call,” then processingcontinues at step 765, otherwise processing continues at step 770.

At step 765, the current asset price (ASSET_PRICE) for the “call” optionis set to the current asset price (ASSET_PRICE) plus the BAND divided bythe dollar amount price movement (TICK). On the other hand, at step 770,the current asset price (ASSET_PRICE) for the “put” option is set to thecurrent price (ASSET_PRICE) minus the BAND divided by the dollar amountprice movement (TICK).

Processing then continues at step 765 or step 770 to step 775.Processing continues at step 775, accesses and receives the extinctiondate for the particular asset (EXT_DATE) which has been set by theexchange and stored by the system administrator from the storage medium250 or 350. Of course, the extinction date could also be manually inputby the user, who could manually input the extinction date set by theexchange each time the system is used. Processing then continues at step780.

At step 780, processing then determines the option premium for theexpirationless option taking into account the extinction band by againusing the option pricing algorithm selected at step 420 and setting thevalue of time until expiration in the algorithm to EXT_DATE. The presentinvention then processing continues at step 799.

At step 799, the present invention proceeds to step 440 of the MainModule at FIG. 4, where it stores the expirationless option premiumunder the variable OPT_PREM at the storage medium 250. At step 450, theprocessing may optionally complete the current financial transaction byissuing a buy or sell hard copy (ticket) to the user which includes theasset premium and other pertinent information related to thetransaction.

In another embodiment, rather than issuing a buy or sell hard copy tothe user, the hard copy may be issued by printing a hard copy to abuyer/seller located in the “trading pit” at the Chicago Exchange, the“desk” at the New York Exchange, or at any other similar destination ofother exchanges throughout the world. Once received by a buyer/seller atan exchange, the buyer/seller may then enter the confirmation order andother information to effect the transfer of any necessary funds upon theclosing of the market, as is customary. In yet another embodiment,rather than issuing a buy or sell hard copy to the user, executing thetransaction may include electronically placing or transferring thetransaction information into a queue of a transaction server along withother transactions. When the queued transaction is removed from thequeue (i.e., by an operator or by a software program), a search for amatching order is performed (e.g., if the executed transaction is a buy,the operator or software program searches for a matching selltransaction). Thus, executing an expirationless option transactionincludes, but is not limited to, issuing a hard copy to the user,issuing a hard copy to a buyer/seller at the exchange, or initiating anautomatic electronic transaction. The present invention anticipates theuse of these and other similar methods for executing the transaction andshould not be limited to any particular method.

The processing then proceeds to step 470, where the user is prompted todetermine whether it wishes to transact another expirationless option.If yes, then the present invention proceeds to step 420, where the useris again prompted by the video display 220 to select an option pricingalgorithm. If no, then the present invention proceeds to step 499, whereit ends the expiration less option transactions for the current user.

Of note, the exemplary embodiment of the present invention assumes that,even though they may not be in actuality, the interest rates anddividend yield associated with each particular asset (e.g., a stock,bond, etc.) are zero. The reason for the assumption is that algorithmsused in connection with pricing the underlying asset already factor theinterest rate and dividend yield into the asset price. These algorithmsmay be either mathematical, inductive or both.

Accordingly, the present invention for transacting an expirationlessoptions using the same algorithms used for expiring options factors theinterest rate and dividend yield into the option premium, but at a valueof zero to ensure both the call and the put option at S=X have a priceequal to the margin requirement.

The following examples illustrate the time/cost relationship betweenexpiring options, premiums, expirationless options and marginrequirements.

Both examples assume a margin requirement of 25%, a current asset priceof $150, a historic price volatility of 35%, and a current risk-freeinterest rate of 6%. Thus, using Black-Scholes algorithm, an impliedtime of 1210.09 days is derived. The first example assumes a call optionwith an exercise price of $60 is requested by the investor.

TABLE 1 Time to Expiring Option Expirationless Margin Expiration PremiumOption Premium Requirement Six Months $2.15 $9.29 $12.5 One Year 4.599.29 12.5 Eighteen Months 6.65 9.29 12.5 Two Years 8.56 9.29 12.5 ThreeYears 11.87 9.29 12.5 Five Years 16.63 9.29 12.5 Ten Years $27.04 $9.29$12.5

The second example assumes a put option with an exercise price Of $40 isrequested by the investor.

TABLE 2 Time to Expiring Option Expirationless Margin Expiration PremiumOption Premium Requirement Six Months 0.85 6.91 12.5 One Year 1.78 6.9112.5 Eighteen Months 2.45 6.91 12.5 Two Years 2.96 6.91 12.5 Three Years3.66 6.91 12.5 Five Years 4.29 6.91 12.5 Ten Years 4.45 6.91 12.5

In yet another embodiment, the method of the current invention may beutilized to calculate an expirationless option premium using asimplified form of an expiring option algorithm. Typical option pricingcalculations require not just a life expectancy of an expirationlessoption, but a volatility assumption over the life of the option as well.This would seem to be impossible over the undetermined time frame of theexpirationless option. However, if the security price already containsan interest rate assumption, we can express the volatility portion ofthe Black-Scholes algorithm in terms of the current price. If we knowthe expirationless put and call must be equal in price, then we cansolve for an implied time to expiration at S=X; and use this impliedtime to solve for option prices at exercise prices other than thecurrent security price.

For an expirationless option, the Black-Scholes formula takes the form:

C=e ^(−dt) S N(dl)−E e ^(−rt) N(d2c)

Where:

-   -   C=Option Premium    -   S=Current stock price    -   E=Option exercise price    -   T=Time to expiration    -   d=Dividend yield    -   r=Risk-free interest rate    -   v=Stock volatility

dl=[ln(S/E)+(r−d+0.5v2)T]/vSQRT(T)

d2=dl−vSQRT(T)

The expirationless call option price can be calculated by settingdividends and the risk-free rate to zero, and setting the exercise priceequal to the stock price. An expirationless option can be calculatedunder any set of assumptions concerning the distribution of prices ofthe underlying security. This method assumes a log normal pricedistribution. It is then possible to calculate the time for which thecall price=the put price=0.5 S. It should be clear that S is the lowestprice to buy the security in the open market. In effect this will be thelower of the actual price or the margin requirement.

The Black-Scholes formula reduces to the following. Note that N is thecumulative normal distribution while NINV is the inverse cumulativenormal distribution. Also, the call price=the put price=0.5 S, and isreferred to as the variable Margin.

$\begin{matrix}{C = {0.5S}} \\{= {{{SN}\left( {d\; l} \right)} - {{SN}\left( {d\; 2} \right)}}}\end{matrix}$ 5.0 = N(d l) − N(d 2) $\begin{matrix}{{dl} = {{\ln \left( {S/S} \right)} + {\left( {0 - 0 + {0.5v^{2}}} \right){T/{{vSQRT}(T)}}} -}} \\{{0.5v^{2}{T/v}\; {{SQRT}(T)}*{{SQRT}(T)}}} \\{= {\left( {0.5v^{2}{{TSQRT}(T)}} \right)/{vT}}} \\{= {0.5{{vSQRT}(T)}}}\end{matrix}$ $\begin{matrix}{{d\; 2} = {{dl} - {{vSQRT}(T)}}} \\{= {{0.5{{vSQRT}(T)}} - {{vSQRT}(T)}}} \\{= {{- 0.5}{{vSQRT}(T)}}}\end{matrix}$

Since:

Margin=N(0.5V SQRT(T))−N(−0.05VSQRT(T))

And N(0.5v SQRT(T)) and N(−0.5v SQRT(T)) are opposing numbers aroundzero, then

Margin/2=N(0.5v SQRT(T))

NINV(Margin/2)=0.5VSQRT(T)

NINV(Margin/2)/0.5V=SQRT(T)

(NINV(Margin/2)/0.5V)² =T

Now that time is purely a function of volatility it can be applied backto the Black-Scholes formula as follows:

 Allowing  x = 2NINV(Margin/2)   and T = (x/v)² = x²/v²$\begin{matrix}{{D\; 1} = {\left\lbrack {{\ln \left( {S/E} \right)} + {5\; v^{2}T}} \right\rbrack/{{vSQRT}(T)}}} \\{= {{\ln \left( {S/E} \right)} + {0.5{{v^{2}\left( {x^{2}/v^{2}} \right)}/{{vSQRT}\left( \left( {x/v} \right)^{2} \right)}}}}} \\{= {\left( {{\ln \left( {S/E} \right)} + {0.5x^{2}}} \right)/x}} \\{= {{{\ln \left( {S/E} \right)}/x} + {0.5x}}}\end{matrix}$ $\begin{matrix}{{D\; 2} = {{Dl} - {v\left( {{SQRT}(T)} \right)}}} \\{= {{dl} - {{vSQRT}\left( ({xlvl}) \right.}}} \\{= {{dl} - x}} \\{= {{{\ln \left( {S/E} \right)}/x} - {0.5x}}}\end{matrix}$

From the equation above for the expirationless option we apply d1 andd2.

EPO=C=SN(ln(S/E)/x+0.5x)−EN(lN(S/E)/x−0.5×)

Therefore, the expirationless option premium can be calculated purely asa function of the stock price and the exercise price and x, where x=2NTNV (Margin/2).

In yet another embodiment, the method of the present invention may beutilized to calculate an expirationless option premium which may then,in turn, be utilized as a basis to determine a premium for aconventional expiring option. Previous methods for pricing expiringoptions have considered the maximum price of an expiring option to bethe price of the underlying security. However, the maximum price of anexpiring option is actually not the price of the underlying security,but is instead the price of an otherwise identical expirationlessoption.

Accordingly, by utilizing the value for an expirationless option asdetermined under the present invention, the price of a traditionalexpiring option can be more accurately calculated. The method fordetermining an expiring option price utilizing an expirationless optionpremium determined according to the method of the present inventionproceeds generally as follows.

First, data representative of the particular asset underlying theexpiring option, the option type (call or put), an exercise price forthe option, the current price of the particular asset underlying theoption, the historic price volatility of the particular asset and themargin requirement for the particular asset are input at step. Then, thecurrent price of the underlying security is used as the expiration priceto solve an expiring option equation (such as the Black-Scholes, theBinomial Pricing, the Finite Difference and the Analytic Approximationalgorithms) for an implied time to expiration. Next, the implied time toexpiration is used as the basis for calculating the price for thecorresponding expirationless option. The expirationless option price isthen used as the maximum price of the corresponding expiring option indetermining the premium for the expiring option.

In regards to an expiration less option, the present invention includesany contingent claim upon the assets, promise of payment, equity,production units or currency of any group, organization, body,institution or collective over any measure of time and any measure ofvalue, regardless of whether the claim has an artificial minimum (floor)or maximum (cap), regardless of whether the claim is contingent uponunforeseeable or controllable action, regardless of whether the claim iscalled by another name, or is characterized as any product, issue orpromise which can be demonstrated to be an individual or series ofoptions, regardless of their life span.

The art has and continues to maintain that the maximum value of anyexpiring option is the underlying product, and that such maximum valueis a determinant in pricing said option, when such statements areclearly false given that expirationless options exist, since the maximumvalue of any expiring option is an otherwise identical non-expiringoption. Given that we have a priority claim on non-expiring options,whose value or price is an integral component of correctly pricingexpiring options, our claim is expanded to cover not only expiringoptions, but any financial product which can be demonstrated to be anindividual or series of options. Expirationless options calculatedaccording to the method of the present invention may also be used inconstructing any combination or permutation of expiring optionscurrently used. For example, these options may include but are notlimited to:

Asian options: average price/rate and strike options.

Barrier options: including knock-out or knock-in, with and withoutrebate.

Binary options: including binary barrier, all-or-none and gap.

Chooser options: which are options to choose a put or call in thefuture.

Compound options: which are options where the underlying security is anoption.

Crack/Spread options: which are options on the distance between pricesof two assets.

Currency translated options: which are foreign exchange optionstranslated into another currency.

Jump options: which are options priced using a jump diffusion process.

Lookback options: which are options based on minimum or maximum pricewithin a certain period.

Rainbow options: which are options on the minimum or maximum of twoassets.

Other miscellaneous options: such as options on U.S. or foreign“stripped” government securities divided into two or more instruments ofprincipal and interest or price and dividend, likewise options onstripped corporate, agency, and municipal securities, notes, bills andCertificates of Deposit; options on Callables, which are securitiescallable at premium or discount; options on Odd-First, -Last, -Middle,or securities with varying coupon/dividend periods; and Options onFutures, Forwards, Currencies, Commodities, Swaps, Debt, Metals, Indicesor any other financial instrument not detailed here.

Even though the present invention has been described substantially interms of utilizing the margin requirement of a margin position in thesecurities market, equivalents to the margin requirement in othermarkets (e.g., earnest money in the real estate market) may be utilized.Further, even though an exemplary embodiment of the present invention isdescribed assuming that the margin requirement on the underlyingsecurity is equal for both the long and short positions, this need notbe the case. Specifically, even in cases where the margin positionrequirements are different, it should be obvious to one of the ordinaryskill in the art that the present invention can be used to determine theexpirationless option premiums comprising each respective position byusing the long position margin requirement for purchasing expirationlesscall options and selling expirationless put options, while using theshort position margin requirement for purchasing expirationless putoptions and selling expirationless call options.

Furthermore, a variety of other financial instruments have been shown tobe equivalent or relatable to options. Therefore, the premiums of eachof these financial instruments may be determined utilizing an expiringor expirationless option premium determined according to the method ofthe present invention. Examples of these option relatable financialinstruments, provided for example and not limitation, include:

Equity: Ownership of a corporation is actually a contingent claim on theassets of the corporation that does not expire and only occurs at a zerostrike price. Thus, equity can be considered to be an option.

Bonds, Loans, Private Placements: These fixed-income instruments areidentical to an individual or series of cash-settled, “capped” calloptions—a call option with a maximum benefit. These options arepurchased with the expectation that the issuer will remain a viable,profitable entity. However, the maximum return on the call is “capped”at some amount (the coupon payment and principal payment at the end ofthe period). One capped option represents each coupon payment as well asthe principal or notional value repaid. Fixed income instruments maytake one of the following forms:

Zero Coupon One payment of principal at end of term.

Floating Rate Coupon: One principal payment at end of term and couponpayments calculated based on an interest rate calculated from someexternal benchmark (90-day Treasury, 90-day LIBOR, etc.)

Level Coupon One principal payment at end of term and coupon paymentsbased on an interest rate agreed at the start of the term.

Amortizing: No principal payment is made during the term of the loan;the principal is repaid over the term as part of the coupon payments.

Forward Contracts: A forward contract obligates its owner to buy a givenasset on a specified date at a price (also known as the exercise price)specified at the origination of the contract This is identical to acombination of a long call option combined with a short put option orvice versa.

Futures Contracts Identical to forward, but typically traded on anexchange where default risk is eliminated by the exchange's guarantee ofperformance.

Swaps: Two parties exchange (“swap”) specified cash flows at specifiedintervals, typically “fixed for floating” or vice versa. A swap contractis really nothing more than a series of forward contracts.

Forward Swap/Delayed Start Swap: A combination of a forward contract anda swap.

Break Forwards: A forward contract with a floor (or a cap) in which thecontract terminates early if prices fall (rise) to a certain level.

Straddles/Strangles/Butterflies: Option combinations that providediffering payoffs based on price movements, typically combinations ofputs and calls, either both long or both short.

Reverse Floating Rate Loan/Bull Floating Rate Notes: If the floatingrate rises, the net coupon payment falls.

Dual Currency Bond: Combination of a standard credit extension with aforward currency contract.

Callable/Puttable Bonds: Standard bond and option on interest rates.

Extendible Notes Long a standard bond and short a call option (issuer).

Puttable Stock Stock issued with puts for investors to acquire more ifthe price falls.

Convertible Bond Bond convertible into shares of the issuing firm.

LYON (Liquid Yield Option Notes): Puttable, callable, convertible, zerocoupon bonds.

Commodity-Linked Bonds: A bond with interest payments linked to somecommodity. Examples include:

Oil-Indexed Notes: Standard note and options on crude oil.

Copper Interest-Indexed Senior Subordinated Notes: Note with quarterlyinterest payments determined by the prevailing price of copper.

Auction Rate Notes/Debentures: Interest rate reset by Dutch auction atthe end of each interest period.

Collateralized Mortgage Obligations (CMOs)/Real Estate MortgageInvestment Conduits (REMICs): Mortgage payment stream divided intoclasses prioritized by rights to receive principal payments.

Commercial Real-Estate Backed Bonds: Nonrecourse bonds serviced andbacked by a specified piece of real estate.

Credit Enhanced Debt Securities: Issuer's obligation to pay is backed byan irrevocable letter of credit or a surety bond.

Dollar BILS: Floating zero coupon notes with interest rates figuredretrospectively on an index of long-term high-grade corporate bonds.

Foreign Exchange Paper: Commercial paper on foreign companies, usuallythose operating under a single currency.

Floating/Rate Sensitive Notes: Coupon rate resets on spread over T-Bill,LIBOR, etc.

Floating Rate Tax-Exempt Revenue Bonds: Coupon rate floats with index(commercial paper, etc.).

Increasing Rate Notes: Coupon rate note increases by specified amount atspecified intervals.

Indexed Currency Option Notes or Principal Exchange Rate LinkedSecurities: Issuer pays reduced/increased principal based onappreciation/depreciation of foreign currency.

Caps/Floors/Collars: Investor who writes a cap (floor/collar) agrees tomake payments when the underlying exceeds the cap (falls below thefloor/outside the collar) or vice versa.

Interest Rate Reset Notes: Rate is reset after issuance to initial rateor some preset rate.

Mortgage Pass-Through Certificates: Undivided interest in a pool ofmortgages.

Negotiable Certificates of Deposit: Registered CDs sold on an agencybasis.

Adjustable Tender Securities: issuer can periodically reset Terms.

Puttable/Extendable Notes: At each period, the issuer can redeem notesat par or extend maturity, notes can be put back to issuer at option ofpurchaser.

Real Yield Securities: Coupon rate resets quarterly, typically to theReal Yield Spread plus some fixed amount.

Receivable Pay-Through Securities: Undivided interest m a pool ofreceivables.

Remarketed Reset Notes: Interest rate resets at end of each period to arate remarketing agent determines will make the notes worth par.

Stripped Mortgage Backed Securities: Coupon payments divided intointerest only and principal only payments to investors.

Stripped Treasuries/Municipals: Divided into coupon & principal (createszero coupon bonds).

Variable Coupon Renewable Notes: Coupon rate varies based on T-Bill,renews every 90 days unless terminated.

Variable Rate Renewable Notes: Coupon rate varies monthly until investorterminates.

Yield Curve/Maximum Rate Notes: Rate is specified at level minus LIBOR(or other standard index/yield).

Adjustable Rate Preferred Stock: Dividend rate resets based onindex/yield.

Auction Rate Preferred Stock: Dividend rate resets by Dutch auction atregular intervals.

Convertible Adjustable Preferred Stock: Convertible into common stock atcertain dates under certain conditions.

Remarketed Preferred Stock (SABRES): Dividend rate resets at the regularintervals to a rate set by the marketing agent to make the preferredstock worth par.

Single Point Adjustable Rate Stock: Dividend rate reset regularly as afixed percentage of some index/yield.

State Rate Auction Preferred Stock: Fixed initial dividend periodfollowed by the issuer's option to convert to a reset by Dutch auctionat periodic intervals.

Variable Cumulative Preferred Stock: Dividend rate reset at issuer'soption to either auction or remarketing method.

Adjustable Rate Convertible Debt: Interest rate vanes directly with theunderlying common stock dividend rate.

Convertible Exchangeable Preferred Stock: Convertible preferred stockexchangeable at issuer's option for debt with identical rate andconversion terms.

Convertible Reset Debentures: Convertible bond with interest rate resetat a predetermined time to an amount sufficient to give debentures amarket value equal to their face amount.

Debt with Mandatory Common Stock Purchase Contracts: Notes that obligatepurchasers to buy sufficient stock from the issuer to retire the issuein full by the scheduled maturity date.

Exchangeable Preferred Stock: Auction rate preferred stock exchanged forauction rate notes.

Synthetic Convertible Debt: Debt and warrants replicating convertibledebt.

Zero Coupon Convertible Debt: Non-interest bearing convertible debt.

Puttable Common Stock: Issue of common stock with the right to put thestock back to the issuer on a specified date at specified price.

Although the present invention has been described in various embodimentsand the various embodiments have been provided as examples ofimplementations of the present invention. It should be understood thatthe present invention is not limited to any particular shape, size,embodiment or configuration. On the contrary, the aspects of the presentinvention can be embodied in various manners within the scope and spiritof the invention as described herein. In addition, the full scope of thevarious embodiments is not limited by the above discussion. Instead, thefull scope of the various embodiments of the present invention shall bemeasured by the appended claims and all equivalents.

All references cited in the present application are incorporated intheir entirety herein by reference to the extent not inconsistentherewith.

It will be seen that the advantages set forth above, and those madeapparent from the foregoing description, are efficiently attained andsince certain changes may be made in the above construction withoutdeparting from the scope of the invention, it is intended that allmatters contained in the foregoing description or shown in theaccompanying drawings shall be interpreted as illustrative and not in alimiting sense.

It is also to be understood that the following claims are intended tocover all of the generic and specific features of the invention hereindescribed, and all statements of the scope of the invention which, as amatter of language, might be said to fall therebetween. Now that theinvention has been described,

1. An apparatus for transacting an expirationless option contractcomprising: an interface for receiving data representative of an optionon an asset, wherein the data includes the value of the underlyingasset; a storage medium in communication with the interface to store thedata received by the interface and an option pricing algorithm; and aprocessor in communication with the storage medium configured to computean option premium on an expirationless option contract using the valueof an underlying asset of the option and an option pricing algorithm,wherein the option contract grants the owner of the option contract aright to sell or buy the underlying asset at a predetermined price. 2.The apparatus of claim 1 wherein the data representative of an option onan asset further includes data selected from the group consisting of anoption type, an exercise price for the particular asset, the historicprice volatility of the particular asset and the margin requirement forthe particular asset and combinations thereof.
 3. The apparatus of claim1 wherein the asset is a security.
 4. The apparatus of claim 3 whereinthe data representative of an option on an asset further includes dataselected from the group consisting of the current market price for thesecurity, an exercise price for the security, the margin price for thesecurity and combinations thereof.
 5. The apparatus of claim 1 whereinthe interface is configured to receive a signal representative of arequest to transact an option on an asset.
 6. The apparatus of claim 1wherein the option pricing algorithm is selected from the groupconsisting of the Black-Scholes, the Binomial Pricing, the FiniteDifference and the Analytic Approximation algorithms.
 7. The apparatusof claim 1 wherein said asset is an option selected from the groupconsisting of: vanilla options; Asian options; barrier options; binaryoptions; chooser options; compound options; crack/spread options;currency translated options; jump options; lookback options; rainbowoptions; options on U.S. or foreign “stripped” government securitiesdivided into two or more instruments of principal and interest or priceand dividend; options on stripped corporate, agency, and municipalsecurities, notes, bills and certificates of deposit; options oncallables; and options on odd-first, -last, -middle, or securities withvarying coupon/dividend periods.
 8. The apparatus of claim 1 whereinsaid asset is selected from the group consisting of: equity, bonds,loans, private placements, forward contracts, futures contracts, swaps,forward swaps/delayed start swaps, break forwards,straddles/strangles/butterflies, reverse floating rate loan/bullfloating rate notes, dual currency bonds, callable/puttable bonds,puttable stock, bond with warrant, convertible bonds, liquid yieldoption notes, commodity-linked bonds, auction rate notes/debentures,collaterallized mortgage obligations/real estate mortgage investmentconduits, commercial real-estate backed bonds, credit enhanced debtsecurities, dollar bills, foreign exchange paper, floating/batesensitive notes, floating rate tax-exempt revenue bonds, increasing ratenotes, indexed currency option notes or principal exchange rate linkedsecurities, caps/floors/collars, interest rate reset notes, mortgagepass-through certificates, negotiable certificates of deposit,adjustable tender securities, puttable/extendable notes, real yieldsecurities, receivable pay-through securities, remarketed reset notes,stripped mortgage backed securities, stripped treasuries/municipals,variable coupon renewable notes, variable rate renewable notes, yieldcurve/maximum rate notes, adjustable rate preferred stock, auction ratepreferred stock, convertible adjustable preferred stock, remarketedpreferred stock, single point adjustable rate stock, state rate auctionpreferred stock, variable cumulative preferred stock, adjustable rateconvertible debt, convertible exchangeable preferred stock, convertiblereset debentures, debt with mandatory common stock purchase contracts,exchangeable preferred stock, synthetic convertible debt, zero couponconvertible debt, puttable common stock.
 9. The apparatus of claim 1wherein the processor is further configured to compute an implied timeusing an option pricing algorithm, the current price of the particularasset, and the margin requirement for the particular asset, the marginrequirement substituted for the option premium and the current pricesubstituted for the exercise price in the calculation of implied timeusing the option pricing algorithm, and wherein the implied time is usedas the time value in the computation of the option premium on anexpirationless option contract.
 10. An apparatus for transacting anexpirationless option contract comprising: an interface for receivingdata representative of an option on an asset, wherein the data includesthe value of the underlying asset; a storage medium in communicationwith the interface to store the data received by the interface and anexpirationless option algorithm; and a processor in communication withthe storage medium configured to compute a price on an expirationlessoption contract using the value of an underlying asset of the option andan option pricing algorithm, wherein the option contract grants theowner of the option contract a right to sell or buy the underlying assetat a predetermined price and wherein the option contract is associatedwith a guarantor, the guarantor providing a guarantee of performance ofthe expirationless options contract by a party other than the issuer ofthe underlying asset.
 11. The apparatus of claim 10 wherein the datarepresentative of an option on an asset further includes data selectedfrom the group consisting of an option type, an exercise price for theparticular asset, the historic price volatility of the particular assetand the margin requirement for the particular asset and combinationsthereof.
 12. The apparatus of claim 10 wherein the asset is a security.13. The apparatus of claim 12 wherein the data representative of anoption on an asset further includes data selected from the groupconsisting of the current market price for the security, an exerciseprice for the security, the margin price for the security andcombinations thereof.
 14. The apparatus of claim 10 wherein theinterface is configured to receive a signal representative of a requestto transact an option on an asset.
 15. The apparatus of claim 10 whereinthe option pricing algorithm is selected from the group consisting ofthe Black-Scholes, the Binomial Pricing, the Finite Difference and theAnalytic Approximation algorithms.
 16. The apparatus of claim 10 whereinthe processor is further configured to compute an implied time using anoption pricing algorithm, the current price of the particular asset, andthe margin requirement for the particular asset, the margin requirementsubstituted for the option premium and the current price substituted forthe exercise price in the calculation of implied time using the optionpricing algorithm, and wherein the implied time is used as the timevalue in the computation of the option premium on an expirationlessoption contract.
 17. An apparatus for transacting an expirationlessoption contract comprising: an interface for receiving datarepresentative of an option on an asset, wherein the data includes thevalue of the underlying asset; a storage medium in communication withthe interface to store the data received by the interface and anexpirationless option algorithm; and a processor in communication withthe storage medium configured to compute a price on an expirationlessoption contract using the value of an underlying asset of the option andan option pricing algorithm, wherein the option contract grants theowner of the option contract a right to sell or buy the underlying assetat a predetermined price, said option contractually coupled to aguarantor, the guarantor providing a guarantee of performance of theexpirationless options contract by a party other than the issuer of theunderlying asset.
 18. The apparatus of claim 17 wherein the datarepresentative of an option on an asset further includes data selectedfrom the group consisting of an option type, an exercise price for theparticular asset, the historic price volatility of the particular assetand the margin requirement for the particular asset and combinationsthereof.
 19. The apparatus of claim 17 wherein the asset is a security.20. The apparatus of claim 19 wherein the data representative of anoption on an asset further includes data selected from the groupconsisting of the current market price for the security, an exerciseprice for the security, the margin price for the security andcombinations thereof.
 21. The apparatus of claim 17 wherein theinterface is configured to receive a signal representative of a requestto transact an option on an asset.
 22. The apparatus of claim 17 whereinthe option pricing algorithm is selected from the group consisting ofthe Black-Scholes, the Binomial Pricing, the Finite Difference and theAnalytic Approximation algorithms.
 23. The apparatus of claim 17 whereinthe processor is further configured to compute an implied time using anoption pricing algorithm, the current price of the particular asset, andthe margin requirement for the particular asset, the margin requirementsubstituted for the option premium and the current price substituted forthe exercise price in the calculation of implied time using the optionpricing algorithm, and wherein the implied time is used as the timevalue in the computation of the option premium on an expirationlessoption contract.
 24. A automated method for transacting an expiringfinancial instrument comprising the steps of: receiving datarepresentative of an asset value for an asset; determining anexpirationless option value for the asset using a computer, theexpirationless option value having a value less than the asset value;computing a premium for the expiring financial instrument using theexpirationless option value; and offering to sell, buy, or trade saidexpiring financial instrument at a price calculated utilizing thecomputed premium.
 25. The method of claim 24, further comprisingproviding a guarantee of performance of said expiring financialinstrument, said guarantee insuring against loss by one party to anoptions transaction resulting from nonperformance of another party tothe options transaction.
 26. The method of claim 24, wherein saidexpiring financial instrument is characterized by being limited tocontingent claims.
 27. The method of claim 24, wherein said expiringfinancial instrument is an American options contract.
 28. The method ofclaim 24, wherein the step of determining an expirationless option valuefor an asset comprises: generating an implied time to expiration usingdata representative of the asset value; and generating a premium for theexpiring financial instrument using the implied time to expiration.